Answer :
Answer:
Yes
Step-by-step explanation:
3 , 4 & 5 are Pythagorean Triplet numbers. When lengths of a triangle's 3 sides are Pythagorean Triplet , the triangle is a right angled triangle.
The triangle will be a right angled triangle only when the hypotenuse will have length of 5 and other 2 sides will have length of either 3 or 4.
Answer:
[tex]\boxed {\boxed {\sf Yes, \ the \ side \ lengths \ 3, \ 4, \ and \ 5\ can \ make \ a \ right \ triangle}}[/tex]
Step-by-step explanation:
If the triangle is a right triangle, then the sides will check out in the Pythagorean Theorem.
[tex]a^2+b^2=c^2[/tex]
Where a and b are the legs and c is the hypotenuse.
1. Define Sides
The legs are the 2 shorter sides and the hypotenuse is the longest.
The sides given are 3, 4 (shorter), and 5 (longest). Therefore:
[tex]a=3 \\b=4 \\c=5[/tex]
2. Check the Sides in the Theorem
Substitute the values into the theorem.
[tex](3)^2+(4)^2=(5)^2[/tex]
Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Addition, and Subtraction.
Solve all of the exponents first.
- (3)² = 3*3= 9
- (4)²= 4*4= 16
[tex]9+16=(5)^2[/tex]
- (5)²= 5*5= 25
[tex]9+16=25[/tex]
Add the numbers on the left side of the equation.
[tex]25=25[/tex]
This is true. 25 is equal to 25, so this triangle can be a right triangle.